For the lesson on July 19, 2011 At Winter Sports School, Mr. Wojo's class Instructor: [name] Lesson plan developed by: [name]

1.Title of the Lesson:

2.Goals of the Lesson:

a. Students will develop strategies to solve problems with 2 unknowns.
b. Students will develop the concept of a solution to a system of equations.

Objectives:
1) Determine the students' prior knowledge of solving systems of equations.
2) Students will be able to solve a problem with 2 unknowns systematically.
3) Students will identify solutions and nonsolutions to a system of equations using graphs,
tables and equations and be able to justify why a particular set of values is a solution.

3.Relationship of the Lesson to the Common Core State Standards

Related prior learning standards (topics/objectives): 8.EE.8. Analyze and solve pairs of simultaneous linear equations.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Solve real-world and mathematical problems leading to two linear equations in two variables.For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Related post learning standards (topics/objectives): A-CED.3.Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A-REI.6.Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.10.Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11.Explain why the x-coordinates of the points where the graphs of the equations y = f(x) andy = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★

4.Unit Plan

Shows how this lesson fits into a larger unit. Briefly describes lessons before and after this lesson.

5.Instruction of the Lesson

This section typically discusses: (a) what the students need to learn according to standards or the curriculum; (b) what the students have learned so far, from observations; (c) the major focus or theme of this lesson; (d) how will accomplish the above objective.

6.Plan of the Lesson

Steps, Learning Activities Teacher’s Questions and Expected Student Reactions

Teacher’s Support

Points of Evaluation

This column shows the major events and flow of the lesson.

This column shows additional moves, questions, or statements that the teacher may need to make to help students.

This column identifies what the teacher should look for to determine whether to proceed, and what observers should look for to determine the effectiveness of the lesson.

Introduction

This section may review ideas from a prior lesson or discuss a simple problem designed to prepare students for work on the main problem.

Part 1: Students will work in pairs on one of the 3 problems below. They will write up/representations of their solutions on chart paper.

A) There are 100 athletes at ? Ski Run. There are only skiers and snowboarders. Find a way to represent all the possible combinations of skiers and snowboarders.

B) There are three times as many skiers as snowboarders at ? Ski Run. Find a way to represent all the possible combinations of skiers and snowboarders.

C) There are 20 more skiers than snowboarders at ? Ski Run. Find a way to represent all the possible combinations of skiers and snowboarders.

Next, each pair of students will briefly present their solution to the class.

Part 2: Brief whole class discussion: Take 2 of the constraints (ex. A and B) and pose the question, "Now can you figure out how many skiers and snowboarders there are?"

Part 3: Jigsaw activity: Re-pair students so that you have a pair who worked on equations A/B, B/C, and C/A. In new pairs, students will find solutions to the problem that combines both their constraints.

It is important to push students towards more than one representation of their problem.

- solutions off a table
- solutions off a graph
- solutions with equation

Both parts of solutions must be stated (number of skiers and number of snowboarders)

Posing the Problem

This section describes a problem as it will be presented to students.

TI-Nspire Activity: "What is a Solution to A System?"
Students will be presented with a calculator and the student activity sheet and will be guided through the lesson.

Printed teacher notes will provide a structure for this part of the lesson.

Teacher will need to determine the entry point to this lesson and emphasize accordingly.

Anticipated Student Responses

This section describes how students might respond to the problem, including incorrect solutions and places where students might get stuck. It can be helpful to tag different responses in some way, e.g. “C1” for Child 1 etc. C1: 2 + (3 * 5) [correct] C2: 3 * 5 = 15; 2 + 15 = 17

Here the lesson might describe how the teacher will handle the different student responses, especially incorrect solutions, students who get stuck, or students who finish early.

4. Comparing and Discussing This section may identify which student solution methods should be shared and in what order, or generally how to handle discussion.

5. Summing up This section may describe how the teacher will summarize the main ideas of the lesson. It may also include an assessment activity.

7.Evaluation

This section often includes questions that the planning team hopes to explore through this lesson and the post-lesson discussion.

For the lesson on July 19, 2011

At Winter Sports School, Mr. Wojo's class

Instructor: [name]

Lesson plan developed by: [name]

1.Title of the Lesson:

a. Students will develop strategies to solve problems with 2 unknowns.2.Goals of the Lesson:b. Students will develop the concept of a solution to a system of equations.

Objectives:1) Determine the students' prior knowledge of solving systems of equations.

2) Students will be able to solve a problem with 2 unknowns systematically.

3) Students will identify solutions and nonsolutions to a system of equations using graphs,

tables and equations and be able to justify why a particular set of values is a solution.

3.Relationship of the Lesson to the Common Core State StandardsRelated prior learning standards (topics/objectives):8.EE.8. Analyze and solve pairs of simultaneous linear equations.

For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.Related post learning standards (topics/objectives):A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) andy = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★

4.Unit PlanShows how this lesson fits into a larger unit. Briefly describes lessons before and after this lesson.5.Instruction of the LessonThis section typically discusses:(a) what the students need to learn according to standards or the curriculum;(b) what the students have learned so far, from observations;(c) the major focus or theme of this lesson;(d) how will accomplish the above objective.6.Plan of the LessonTeacher’s Questions and Expected Student Reactions

This column shows the major events and flow of the lesson.This column shows additional moves, questions, or statements that the teacher may need to make to help students.This column identifies what the teacher should look for to determine whether to proceed, and what observers should look for to determine the effectiveness of the lesson.IntroductionThis section may review ideas from a prior lesson or discuss a simple problem designed to prepare students for work on the main problem.Part 1: Students will work in pairs on one of the 3 problems below. They will write up/representations of their solutions on chart paper.

A) There are 100 athletes at ? Ski Run. There are only skiers and snowboarders. Find a way to represent all the possible combinations of skiers and snowboarders.B) There are three times as many skiers as snowboarders at ? Ski Run. Find a way to represent all the possible combinations of skiers and snowboarders.C) There are 20 more skiers than snowboarders at ? Ski Run. Find a way to represent all the possible combinations of skiers and snowboarders.Next, each pair of students will briefly present their solution to the class.

Part 2: Brief whole class discussion: Take 2 of the constraints (ex. A and B) and pose the question, "Now can you figure out how many skiers and snowboarders there are?"

Part 3: Jigsaw activity: Re-pair students so that you have a pair who worked on equations A/B, B/C, and C/A. In new pairs, students will find solutions to the problem that combines both their constraints.

- solutions off a table

- solutions off a graph

- solutions with equation

Posing the ProblemThis section describes a problem as it will be presented to students.TI-Nspire Activity: "What is a Solution to A System?"

Students will be presented with a calculator and the student activity sheet and will be guided through the lesson.

Anticipated Student ResponsesThis section describes how students might respond to the problem, including incorrect solutions and places where students might get stuck. It can be helpful to tag different responses in some way, e.g. “C1” for Child 1 etc.C1: 2 + (3 * 5) [correct]C2: 3 * 5 = 15; 2 + 15 = 17Here the lesson might describe how the teacher will handle the different student responses, especially incorrect solutions, students who get stuck, or students who finish early.4. Comparing and DiscussingThis section may identify which student solution methods should be shared and in what order, or generally how to handle discussion.5. Summing upThis section may describe how the teacher will summarize the main ideas of the lesson. It may also include an assessment activity.

This section often includes questions that the planning team hopes to explore through this lesson and the post-lesson discussion.7.Evaluation